02ps04 New Variance Solution

0:00  0:03The answer is a ½ or 0.5

0:03  0:08To see, let us multiply these two gaussians over here

0:08  0:11which the exponent becomes an addition

0:11  0:13we can now rewrite this as follows

0:13  0:19when we bring the factor 2, for these two terms in to the numerator

0:19  0:21as our 2 sigma square,

0:21  0:25and from that we see that the new variance is 0.5

0:25  0:29as large as the old one when applied to the squares.

0:29 So, as a result, you would have this equation over here.
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